A057708 Numbers m such that 2^m reversed is prime.

1, 4, 5, 7, 10, 17, 24, 37, 45, 55, 70, 77, 107, 137, 150, 271, 364, 1157, 1656, 2004, 2126, 3033, 3489, 3645, 4336, 6597, 7279, 12690, 13840, 20108, 21693, 28888, 84155, 102930

Offset

1,2

Comments

a(35) > 105000. - Giovanni Resta, Feb 22 2013

From Bernard Schott, Jan 30 2022: (Start)

If m is an even term, then u = m/2 is a term of A350441, this because 2^m = 4^(m/2). In fact, terms of A350441 are half the even terms of this sequence here.

If m is a term multiple of 3, then k = m/3 is a term of A350442, this because 2^m = 8^(m/3). First examples: m = 24, 45, 150, 1656, ... and corresponding k = 8, 15, 50, 552, ... (End)

Links

Table of n, a(n) for n=1..34.

Example

4 is a term because 2^4 reversed is 61 and prime.

Maple

with(numtheory): myarray := []: for n from 1 to 4000 do it1 := convert(2^n, base, 10): it2 := sum(10^(nops(it1)-i)*it1[i], i=1..nops(it1)): if isprime(it2) then printf(`%d, `, n) fi: od:

Mathematica

Do[ If[ PrimeQ[ FromDigits[ Reverse[ IntegerDigits[2^n]] ]], Print[ n]], {n, 20000}] (* Robert G. Wilson v, Jan 29 2005 *)
Select[Range[4400], PrimeQ[IntegerReverse[2^#]]&] (* Requires Mathematica version 10 or later *) (* The program generates the first 25 terms of the sequence; to generate more, increase the Range constant, but the program will take longer to run. *) (* Harvey P. Dale, Aug 05 2020 *)

Prog

(Python)
from sympy import isprime
k, m, A057708_list = 1, 2,  []
while k <= 10**3:
    if isprime(int(str(m)[::-1])):
        A057708_list.append(k)
    k += 1
    m *= 2 # Chai Wah Wu, Mar 09 2021
(PARI) isok(m) = isprime(fromdigits(Vecrev(digits(2^m)))) \\ Mohammed Yaseen, Jul 20 2022

Crossrefs

Cf. A004094, A341713.

Numbers m such that k^m reversed is prime: this sequence (k=2), A350441 (k=4), A058993 (k=5), A058994 (k=7), A350442 (k=8), A058995 (k=13).

Sequence in context: A145018 A018910 A022936 * A032686 A074300 A344157

Adjacent sequences: A057705 A057706 A057707 * A057709 A057710 A057711

Keyword

base,nonn,more

Author

G. L. Honaker, Jr., Oct 23 2000

Extensions

More terms from Chris Nash (chris_nash(AT)prodigy.net), Oct 25 2000

Two more terms from Robert G. Wilson v, Jan 29 2001

3 more terms from Farideh Firoozbakht, Aug 05 2004

a(33)-a(34) from Giovanni Resta, Feb 22 2013

Status

approved